# How do you rationalize the denominator and simplify 2/(2sqrt3-4)?

May 1, 2018

$- \sqrt{3} + 2$

#### Explanation:

$\frac{2}{2 \sqrt{3} - 4}$

First, factor $2$ from the denominator:
$\frac{2}{2 \left(\sqrt{3} - 2\right)}$

Both numerator and denominator have a $2$, so we can cancel them out:
$\frac{1}{\sqrt{3} - 2}$

To rationalize the denominator, we multiply both numerator and denominator it by its conjugate, or $\sqrt{3} + 2$.

Let's do that:
$\frac{1}{\sqrt{3} - 2} \textcolor{b l u e}{\times \frac{\sqrt{3} + 2}{\sqrt{3} + 2}}$

Simplify:
$\frac{\sqrt{3} - 2}{{\sqrt{3}}^{2} - 2 \sqrt{3} + 2 \sqrt{3} - {2}^{2}}$

$\frac{\sqrt{3} - 2}{3 - 4}$

$\frac{\sqrt{3} - 2}{- 1}$

$- \left(\sqrt{3} - 2\right)$

$- \sqrt{3} + 2$